Elementary Theory of Angular Momentum. By M. E. Rose. Pp. x, 248. 80s. 1957. (Wiley)

The low value of , where is the nematic-isotropic phase transition temperature and denotes the virtual transition temperature, is a long-standing puzzle in the physics of liquid crystals. The present review presents experimental and theoretical results on this long-standing problem. New experimental and theoretical results for the critical behaviour in the isotropic phase of nematogens are reviewed. We calculate in a unified approach the low value of , at both critical and tricritical points. The possibility of tricritical behaviour at the nematic-isotropic transition is also discussed by means of Landau theory. The various predictions are compared with the available experimental results.

http://iopscience.iop.org/article/10.1088/0953-8984/10/41/003/pdf

The puzzle of the nematic-isotropic phase transition

Modulated differential scanning calorimetry (MDSC) has been used to obtain specific heat measurements on octyloxycyanobiphenyl (8OCB), octylcyanobiphenyl (8CB) and nonyloxycyanobiphenyl (9OCB) liquid crystals and on several binary mixtures of 8OCB + 9OCB and 8CB + 9OCB. The order of the mesophase transitions, smectic A(SmA) to nematic(N) and N to isotropic (I) on pure components and on binary mixtures has been studied and, in addition, both binary mesophase diagrams have been built. For each set of mixtures, there exists a tricritical point (TCP) composition at the SmA–N transition. The TCP compositions have been found to be X9OCB = 0.63 for the system 8OCB + 9OCB and X9OCB = 0.42 for the system 8CB + 9OCB. In addition, the specific heat
critical exponents (α) through second order SmA to N transition have been obtained between 8OCB(or 8CB) and the TCP composition for the two sets of binary mixtures. When these α-values were plotted against the normalised nematic range, a common and uniform crossover trend was found. Indeed, this fact suggests a uniform behaviour in terms of the McMillan ratio for the nCB and nOCB series of liquid crystals. Moreover, for these compounds there exists a common value of (TAN/TNI)TCP of 0.99 and also a value of (TAN/TNI)3D-XY of about 0.96.

Binary mixtures of nCB and nOCB liquid crystals. Two experimental evidences for a smectic A nematic tricritical point

Different kind of measurements were performed on the liquid crystal nonyloxycyanobiphenyl (9OCB) to carry out a study of the molecular dynamics in the smectic A (SmA), nematic (N), and isotropic (I) phases as well as an exhaustive analysis of both the SmA-to-N and N-to-I phase transitions. For the dynamic study, broadband dielectric spectroscopy (102 to 1.8 × 109 Hz) was used. Two orientations (parallel and perpendicular) of the molecular director with regard to the probing electric field were investigated. From this study, the static dielectric permittivity was obtained in both alignments and, in addition, the molecular motions that contribute to each one were discussed. The static dielectric data together with specific heat and volumetric determinations were analyzed, proving that both phase transitions are weakly first order, displaying a nearly tricritical behavior. However, the width of metastable regions seems to be dependent on the physical magnitude, although specific heat and volumetric determina...

Critical behavior and scaling relationships at the SmA(d)-N and N-I transitions in nonyloxycyanobiphenyl (9OCB).

Finite size scaling in the planar Lebwohl–Lasher model

We determine the nematic-isotropic coexistence curve terminating at the critical point in a temperature-external field phase diagram for nematic liquid crystals with positive diamagnetic anisotropy, where the molecules are either perfectly uniaxial or biaxial using computer simulation of a lattice model. The coexistence curve is much steeper than that predicted by the standard Landau--de Gennes and Maier-Saupe mean-field theories. For the uniaxial system the critical magnetic field is estimated to be one order of magnitude lower than the mean-field estimate but of the same order of magnitude as the experimental measurement. Our study shows that molecular biaxiality could reduce the critical field strength significantly.

Effect of an external magnetic field on the nematic-isotropic phase transition in mesogenic systems of uniaxial and biaxial molecules: a Monte Carlo study.

Monte Carlo simulation of joint density of states in one-dimensional Lebwohl–Lasher model using Wang–Landau algorithm

Density effects at the nematic–isotropic phase transition is studied by means of Landau–de Gennes theory. The analysis shows that the density variation shifts the nematic–isotropic transition temperature TNI and changes the Landau–de gennes free energy expansion coefficients. The possibility of the tricritical behaviour of the nematic–isotropic phase transition is also discussed by the density variation. The low value of TNI-T* (T* is the absolute stability limit of the isotropic phase) and the various thermodynamic quantities are also calculated to compare with the experimental data.

Density Effects in the Landau-De Gennes Theory Near the Nematic-Isotropic Phase Transition

We propose a Landau-de Gennes phenomenological model to describe the pressure induced smectic A-nematic phase transition. The influence of pressure on smectic A-nematic phase transitions are discussed for varying coupling between orientational and translational order parameter with pressure. Increasing the pressure, the first order nematic-smectic A transition becomes second order at a tricritical point which agrees fairly well with available experimental results.

Kisor Mukhopadhyay

Papers

Effect of an external magnetic field on the nematic-isotropic phase transition in mesogenic systems of uniaxial and biaxial molecules: a Monte Carlo study.

Monte Carlo simulation of joint density of states in one-dimensional Lebwohl–Lasher model using Wang–Landau algorithm

Density Effects in the Landau-De Gennes Theory Near the Nematic-Isotropic Phase Transition

Influence of Pressure on Smectic A-Nematic Phase Transition

Study of a planar lattice model with P4 interaction